Oscillates in the area of ​​the square

Abstract

In this article we examine how to approximately infer the area of ​​the region in the $xy$ plane bounded by the graph of the function $x\in[0,1]\mapsto 1+\frac{1}{n}sin(x\sqrt{n}) $, $n\in\mathbb{N}$, and along the $x$ and $y$ axes, and along the line $x=1$ using elements from Elementary Mathematics (covered in Basic Education). We also show how this analysis can be considered for the approximate calculation of areas of flat figures obtained by varying the sides of polygons via trigonometric functions; To this end, we define the notion of functions with good oscillatory behavior. We obtain formulas using geometric concepts from plane geometry aimed at activities at the Basic Education level. We use the graphic packages \LaTeX\ 'animate', 'tikz', 'tkz-euclide' and 'pgfplots' to produce figures and animations.